BYLINE: Perimeter Institute for Theoretical Physics
Newswise — Humans intuitively understand gravity. The closer we get to massive body, the more we feel the gravitational pull. The further away we get from that mass, the less grip it has.
But at the heart of an atom, where the “strong force” shapes the behaviour of quarks and gluons, something counterintuitive happens.
The closer quarks and gluons are to one another, the more freely they move about. Yet if they try to move further apart from each other, the force gets dramatically stronger.
In that sense, it is the opposite of the way gravity works. And it’s the reason your table, you chair, your computer — and you! — don’t fly apart. Despite the positive charges in the nuclei of atoms, these particles remain tightly bound together.
It was clear in the early 20th century that the atom consisted of electrons orbiting a positively charged nucleus, and that there must be a strong force holding the nucleus together and overcome the electromagnetic repulsion.
But it wasn’t until the deep inelastic scattering experiments at the Stanford Linear Accelerator (SLAC) in the late 1960s and early 1970s that scientists had the first experimental evidence that protons are made of smaller, point-like constituents (quarks and gluons, collectively called partons). As crucially, these experiments showed that particles in nuclei can move freely around when they are close to each other yet become tightly bound if they move away from one another.
But still, the question was: Why?
Our understanding deepened in the 1970s, when scientists David Gross, Frank Wilczek, and independently David Politzer, discovered how “asymptotic freedom” works in the theory of the strong interactions. They described clearly how the strength of the strong force changes with distance or energy (what physicists call scale dependence), a discovery that won them the Nobel Prize in 2004.
Coming out of their equations was the (mathematically) famous 11/3 factor in the one loop beta function. It comes from detailed calculations of the quantum fluctuations involving gluon loops in the nucleus. It is at the heart of the modern day version of quantum chromodynamics, our current best description of the strong force in the nuclei of atoms.
A new mathematical tool
Nevertheless, the calculations for interacting gluons and quarks are notoriously difficult, especially when using tools like Feynman diagrams.
But recently, two mathematical physics researchers at Perimeter Institute — faculty member and Krembil William Rowan Hamilton Chair Kevin Costello, and postdoctoral researcher Roland Bittleston —developed a new tool for doing this, using an “index theorem on twistor space.”
Twistor theory is a mathematical framework which recasts complicated physical fields on a space-time in terms of simple algebraic data. Meanwhile, index theory bridges analysis and topology. It can answer analytic questions, for example, ‘how many solutions does a certain differential equation have?’ in terms of the topology, or shape, of a space.
Costello says twister theory provides a way of taking complicated equations and making them simpler. Bittleston adds that scale symmetries do not usually have an interesting topology, but on twistor space scale symmetry wraps into a circle, which does have an interesting topology.
The new mathematical tool that Costello and Bittleston have devised makes the process of understanding what is happening in the nuclei of atoms computationally easier. The paper on their approach, One-Loop QCD
